$A$ ball of mass $2 \,kg$ is thrown from a tall building with velocity $v = (20 \,m/s) \hat{i} + (24 \,m/s) \hat{j}$ at time $t = 0 \,s$. The change in the potential energy of the ball after $t = 8 \,s$ is (The ball is assumed to be in air during its motion between $0 \,s$ and $8 \,s$, $\hat{i}$ is along the horizontal and $\hat{j}$ is along the vertical direction. Take $g = 10 \,m/s^2$). (in $\,kJ$)

Block $A$ of mass $m$ is hanging from a vertical spring of spring constant $k$ and is at rest. Block $B$ of mass $m$ strikes block $A$ with velocity $v$ and sticks to it. The velocity $v$ for which the spring just attains its natural length is:

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
$(a)$ Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
$(b)$ Work done by gravitational force in the above case.
$(c)$ Work done by friction on a body sliding down an inclined plane.
$(d)$ Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.
$(e)$ Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

The friction coefficient between the horizontal surface and each of the blocks shown in the figure is $\mu = 0.2$. The collision between the blocks is perfectly elastic. What is the separation between the blocks when they come to rest? (in $cm$)

Two identical balls of mass $2 \ kg$ are moving towards each other with a velocity of $5 \ m/s$. They collide and come to rest after the collision. What is the work done by the internal forces in $J$?

$A$ block of weight $10 \ N$ slides down a curved track $AB$ and then onto a rough horizontal surface. The coefficient of kinetic friction between the block and the rough surface is $0.20$. If the block starts sliding from a height of $1.0 \ m$ above the horizontal surface,calculate the distance $S$ it travels on the rough surface before coming to rest. [$g = 10 \ m \ s^{-2}$]